Chen, Bo (2010). THE GABRIEL-ROITER SUBMODULES OF SIMPLE HOMOGENEOUS MODULES. Proc. Amer. Math. Soc., 138 (10). S. 3415 - 3425. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 0002-9939
Full text not available from this repository.Abstract
Let Lambda be a connected tame hereditary algebra over an algebraically closed field. We show that if Lambda = kQ is of type (A) over tilde (n), (D) over tilde (n), (E) over tilde (6) or (E) over tilde (7), then every Gabriel-Roiter submodule of a quasi-simple module of rank I (i.e. a simple homogeneous module) has defect -1. In particular, any Gabriel-Roiter submodule of a simple homogeneous module yields a Kronecker pair, and thus induces a full exact embedding of the category mod k (A) over tilde (1) into mod Lambda, where (A) over tilde (1) is the Kronecker quiver. Consequently, we obtain that all quasi-simple modules are Gabriel-Roiter factor modules.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-496229 | ||||||||
| DOI: | 10.1090/S0002-9939-2010-10243-5 | ||||||||
| Journal or Publication Title: | Proc. Amer. Math. Soc. | ||||||||
| Volume: | 138 | ||||||||
| Number: | 10 | ||||||||
| Page Range: | S. 3415 - 3425 | ||||||||
| Date: | 2010 | ||||||||
| Publisher: | AMER MATHEMATICAL SOC | ||||||||
| Place of Publication: | PROVIDENCE | ||||||||
| ISSN: | 0002-9939 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/49622 |
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